That’s why these next four games could wind up being critical to his future as the Giants’ coach. After three seasons without making the playoffs, if the Giants can’t get there this year — and through this weak division — there is a mounting feeling that the franchise might need a change.

Coughlin’s response to that?

“I don’t pay any attention to it,” he said when the subject of his job security was broached on Monday.

That doesn’t mean it does not exist. The Giants lost to the Jaguars a year ago, and John Mara later said he left that game feeling as if he wanted to “fire everybody.”

As Mara silently walked through the Giants’ locker room Sunday evening, he had a similar look of disgust on his face. Whether he will act on that impulse a month from now remains to be seen, but Coughlin insists that he is not affected by the speculation or even the reality of the possibility.

“I’m trying to stay focused for the benefit of my team and my coaches and everybody else,” he said.

Giants videos

Coughlin said it is “pretty frustrating” that each time he makes a critical decision in a game, it is sabotaged by a lack of execution. That again was the case Sunday. Midway through the fourth quarter, on fourth-and-2 at the Jets’ 4, Coughlin decided to go for a touchdown and a 17-point lead rather than kick a field goal for a 13-point lead. Eli Manning threw an interception, the Giants came away without scoring and up by 10, and the Jets scored the game’s final 13 points.

It was the fifth time this season the Giants have lost a game they led in the final two minutes of regulation. Those losses have come by a combined 12 points.

“The majority of what we’ve done is to try to put ourselves in position where that last drive is not going to put us in the situation we’ve been in four or five times,’’ Coughlin said. “Obviously, that hasn’t happened. We’ve tried for touchdowns instead of field goals, and it hasn’t happened.”

Coughlin defended his decisions. “Quite frankly, you can all disagree, but we’re trying to win games the best way we can,” he said. “To be honest with you, nobody knows my team better than I know my team. So when you sit in judgment of what goes on, it’s all been thought out whether you like it or not, whether it’s right or wrong.”

So what is a head coach to do when every button he presses seems to open a trap door beneath him?

“Keep coaching,” he said. “Keep working. Keep fighting. Keep planning. Keep deciding. Keep making decisions based on what we have and be aggressive. Don’t sit back because the world thinks it’s not getting done.”

The Giants — who are tied with Washington and the Eagles for first place at 5-7 — still could win the division title, even if they merely split their final four games and finish 7-9 (two seven-win teams have made the playoffs since 2010). Coughlin has been driving that fact home to the despondent players.

“We’re all sick of losing,” he said. “We have to find a way to win a game and change this negativity . . . get our momentum going in the right direction.”

Time is running out on the Giants’ season, and, quite possibly, Coughlin’s tenure.